Problem: Simplify; express your answer in exponential form. Assume $q\neq 0, p\neq 0$. $\dfrac{{(q^{3})^{5}}}{{(q^{3}p^{5})^{5}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${q^{3}}$ to the exponent ${5}$ . Now ${3 \times 5 = 15}$ , so ${(q^{3})^{5} = q^{15}}$ In the denominator, we can use the distributive property of exponents. ${(q^{3}p^{5})^{5} = (q^{3})^{5}(p^{5})^{5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(q^{3})^{5}}}{{(q^{3}p^{5})^{5}}} = \dfrac{{q^{15}}}{{q^{15}p^{25}}}$ Break up the equation by variable and simplify. $\dfrac{{q^{15}}}{{q^{15}p^{25}}} = \dfrac{{q^{15}}}{{q^{15}}} \cdot \dfrac{{1}}{{p^{25}}} = q^{{15} - {15}} \cdot p^{- {25}} = p^{-25}$.